arXiv:2606.22566cs.CEcs.LG2026-06

用深度网络加速压电复合材料性能预测,算得快还准。

Deep material network for homogenization of piezoelectric composites

论文配图:Deep material network for homogenization of piezoelectric composites
图 1 · 摘自论文原文
  • 构建物理驱动的深度网络,直接嵌入电-力耦合机理。
  • 相比传统模拟,计算速度提升300倍以上,精度高。
  • 适合压电材料设计与多尺度仿真,尤其擅长非线性场景。

压电复合材料因其可调的电-力性能,广泛应用于传感器、执行器和能量采集器件中。然而,基于直接数值模拟(DNS)的传统计算均质化方法计算成本高昂,尤其在需要重复分析的多尺度仿真与材料设计任务中。为此,本文提出一种压电深材料网络(PDMN),用于高效均质化双相压电复合材料。该框架将电-力均质化控制关系直接嵌入网络结构,形成物理信息驱动的半解析代理模型,显式捕捉各组分间电场与应力的双向耦合。网络在离线阶段基于线性电弹性数据集训练,并通过全耦合牛顿-拉夫逊求解与一致电-力切线,在更广的本构条件下实现高效在线预测,包括非线性电弹性及历史依赖响应。验证案例包括聚偏氟乙烯(PVDF)与铌酸锂(LiNbO₃)在反向相布局下的非线性电弹性加载,以及具有耦合应力松弛的粘弹性-压电复合材料。数值结果表明,所提PDMN在保持高预测精度的同时,相较DNS将计算成本降低超过三个数量级。因此,该框架为压电复合材料的多尺度分析与设计提供了高效可靠的替代方案。

原文摘要 · Abstract (English)

Piezoelectric composites are widely used in sensors, actuators, transducers, and energy-harvesting devices because their effective electromechanical performance can be tailored by combining constituent phases and microstructural architecture. However, conventional computational homogenization based on direct numerical simulation (DNS) is computationally expensive, particularly for multiscale simulations and material design tasks that require repeated homogenization analyses. To address this limitation, this work proposes a piezoelectric deep material network (PDMN) to efficiently homogenize two-phase piezoelectric composites. The proposed framework embeds the governing electromechanical homogenization relations directly into the network architecture, yielding a physics-informed, semi-analytical surrogate that explicitly captures the two-way coupling between the mechanical and electrical fields across constituent phases. The network is trained offline on linear electroelastic datasets and, through a fully coupled Newton--Raphson solution with a consistent electromechanical tangent, subsequently used for efficient online prediction under broader constitutive settings, including nonlinear electroelasticity and history-dependent responses. The framework is validated on two-phase composites of polyvinylidene fluoride (PVDF) and lithium niobate (LiNbO$_3$) with reversed phase arrangements under nonlinear electroelastic loading, and on a viscoelastic--piezoelectric composite exhibiting coupled stress relaxation. Numerical examples show that the proposed PDMN achieves high predictive accuracy while reducing the computational cost by more than three orders of magnitude compared with DNS. The proposed framework, therefore, provides an efficient and reliable surrogate for the multiscale analysis and design of piezoelectric composites.

压电材料深度学习多尺度仿真电-力耦合

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